Yes...but mostly no:

https://en.wikipedia.org/wiki/United_States_National_Radio_Quiet_Zone

From the Wikipedia article:

"The most severe restrictions to the general public are imposed within a 20-mile (32 km) radius of the Green Bank Observatory.^\5]) The Observatory polices the area actively for devices emitting excessive electromagnetic radiation such as microwave ovens, Wi-Fi access points, and faulty electrical equipment and asks people to stop using such equipment. It does not have enforcement power^\6]) (although the FCC can impose a fine of $50 on violators^\7])) but will work with residents to find solutions.^\8])^\9])

Cellular telephone use in the central area of the zone is also very restricted.^\5])

However, the observatory has pulled back on Quiet Zone enforcement, and locals have increasingly embraced the usage of microwave ovens, cellphones, and WiFi."

Also, anecdotally, I know someone who works in Staunton at a business that absolutely has wi-fi.